Why did the Gaon do this? Do you realize what that means to the Gaon? Bishlema the Gemara (Megilla 3a) says מכאן סמכו של בית רבי שמבטלין תלמוד תורה ובאין לשמוע מקרא מגילה, so we're mevateil Torah for the Megilla. And Bishlema the Bach in the beginning of OC 695 says that the makor for a lengthy seuda is the story (Megilla 7a) about the talmidim whose absence from the shiur on Purim on Purim was excused by saying they were busy with the meal- רב אשי הוה יתיב קמיה דאמימר נגה ולא אתו רבנן אמר ליה מאי טעמא לא אתו רבנן דלמא טרידי בסעודת פורים. But that just means 'longer than usual.' But the whole day??? How is this seuda different than any other seudas hoda'ah, or seudas yomtov?
It seems to me that the Gaon held that the same way there's a din of כל המרבה לספר by the Seder, which the Tanna'im, as a middas chasidus, continued the entire night until זמן קריאת שמע של שחרית, so too there is a middas chasidus to sit the whole day at the seder. But do we know why the Seder has this unique halacha? I don't. But if you do, maybe it will shed light on the Gaon's hanhaga on Purim.
Another possible lead is the Gemara in Sukka 41b, that says that the Men of Yerushalayim used to carry the Lulav around with them the whole day, even though they were yotzei in the first moment of picking it up, and did the na'anu'im early in the morning, because they were diligent in the Mitzvos-
To answer this question, I would suggest that there is a basic difference between the seudos of other Yamim Tovim and the Seuda of Purim. The other seudos are a fulfillment of the mitzva of Simcha and Oneg. How do you have simcha and oneg? By eating a festive meal. On Purim, it's not only the din of Simcha, it's a din of eating per se, that having a festive meal is itself the mitzvas hayom, to commemorate the meal with Achashveirosh that began our downfall and Esther's meal that ended it. So on Yomtov, even according to the hanhaga of the Anshei Yerushalayim there's no ma'alah of a day long seuda, because the eating is not the cheftza shel mitzva. But on Purim when the eating is the mitzva itself, then doing the mitzva the whole day is exactly what the Anshei Yerushalayim did with their Lulavim. I am told that the Brisker Rov also says this distinction between Seudas Yomtov and Seudas Purim. I haven't seen it inside.
Dr. Meir Zahtz suggested that because Purim is seen as the חציו לכם aspect of Yom Kippur, the same way the din Taanis of Yom Kippur is in force the entire day without interruption, so too the mitzvas Lachem of Purim, the Seuda, is in force the entire day without interruption. Dr. Zahtz gets points for ingenuity. His pshat is especially good in light of the Gaon who quotes the Gemara in Pesachim 68b that מר בריה דרבינא fasted every day of the year with three (3) exceptions: Erev Yom Kippur, Purim, and Shavuos. The Gaon (I don't have the Mareh Makom, but it's common knowledge, and Rav Hutner brings it down in Pachad Yitzchak Purim #8) says pshat that each of these three days is a day of Kabbalas Hatorah, and that the two days, Purim and Yom Hakipurim, are inextricably tied together, as Meir said, with one functioning as the חציו לכם and the other as the חציו לשם. The Zohar also says that each day serves as a השלמה for the other. But his teretz doesn't appeal to me from a Gaon standpoint- it's a fine reason for a Rebbe to sit at the table and eat a whole day, but it's not a good enough reason for the Gaon to sit at the table the whole day.